Describing Many-Particle Quantum Systems

N.P. Klepikov

An active transformation of a physical system implies its motion. A passive transformation of the system is a change in the method of describing it. An analogy transformation means transition to another physical system, similar in some respect to the original one. In some cases transformations of one type may imitate those of another. The operation of particle permutation in quantum mechanics implies a passive transition to describing the same state of the system by a different method of introducing particle numbering. The problems of transitions from describing identical particles to describing different ones and that of explaining the probabilistic meaning of wave functions statistically are touched upon.

Philip L. Bowers

Ajit Kumar

Azzouz Zinoun, Jean Cortois

Algebraical structures that characterize different statistics for describing a system of particles are represented by equivalence classes of bilinear maps. Theorems that connect these structures are presented.

Bruce M. Boghosian, Washington Taylor

We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schroedinger particle and the eigenvalues of a unitary matrix describing the local evolution of the model. Second quantized versions of these unitary models can be defined, describing in the continuum limit the evolution of a nonrelativistic quantum many-body theory. An arbitrary potential is easily incorporated into these systems. The models we describe fall in the class of quantum lattice gas automata, and can be implemented on a quantum computer with a speedup exponential in the number of particles in the system. This gives an efficient algorithm for simulating general nonrelativistic interacting quantum many-body systems on a quantum computer.

W. D. Kraeft, D. Kremp, W. Ebeling +1 more